Question

Please help
Solve for x
sin(2x)=cos(3x)
I did it by expanding everything with double angle and addition identities but I ended up with
2sin(x)+2sin^2(x)-cos(x)=-1
Not sure where to go or if there is an easier way to do it

Answer 1

hmm, lots of properties to use prolly

Answer 2

sin(2x)=cos(3x)

2*sin(x)*cos(x) = cos(2x + x) , what was the cox(x+y)= thing?

Answer 3

i think i have it, if you return

Answer 4

Sorry I left
But anyway that's what I did and I ended up with 2sin(x)+2sin^2(x)-cos(x)=-1

Answer 5

And I did that by writing out the result of the cos(2x+x) and getting cos^2(x)-cos(x)-2sin^2(x)cos(x)
I then factored out the cos(x) since it was a common factor
On the LHS I got 2sin(x)cos(x) and then I divide both sides by cos(x)
Getting 2sin(x)=cos(x)-1-2sin^2(x)
Then I left the -1 on the RHS and put the other two terms onto the LHS
Getting 2sin(x)+2sin^2(x)-cos(x)=-1

Answer 6

2*sin(x)*cos(x) = cos(2x + x)

2*sin(x)*cos(x) = cos(2x)*cos(x) - sin(2x)*sin(x)

2*sin(x)*cos(x) = ( 1 - 2sin^2(x))*cos(x) - 2*sin(x)*cos(x)*sin(x)

2*sin(x)*cos(x) = cos(x) - 2sin^2(x)*cos(x) - 2sin^2(x)*cos(x)


2sin(x) = 1 - 4sin^2(x)


i think that is it,, solve quadratic

Answer 7

Yeah thanks I'll try it

Answer 8

not sure if it supposed to be a 'nice' angles or not

Answer 9

No it's not
They're supposed to be complicated lol

Answer 10

4u^2 + 2u - 1 = 0

Answer 11

sin(x) = ......

Answer 12

yeah no,, goodluck

Answer 13

Um just checking that's supposed to be 3 and not 4 right?

Answer 14

i was just looking over the linked sheet, the cofunctions formula... sin(x)=cos(pi/2 - x)

maybe replace the sin(2x) with cos(pi/2 - 2x)


cos(pi/2 - 2x) = cos(3x)

Answer 15

pi/2 - 2x = 3x

Answer 16

if that is legal, .. and cos(angle) is symmetric for + or - angle, so set that to +3x and -3x

Answer 17

i think i did this prob before on here sometime, or something like it

Answer 18

@brill no, 4, 3rd line in the thing, you distribute, and have -2 and a -2

Answer 19

Oh yeah you're right, forgot the two whoops

Answer 20

Thanks! I solved it using quadratic formula.

Answer 21

cool, check to see if that second method also is the same answer... brb in a few

Answer 22

Yeah I tried it but the most I could take it is a -sin(x)=cos(x)-4sin^2(x)cos(x)